JP2021056503A - Diffusion element - Google Patents

Abstract

To provide a diffusion element which makes optical intensity uniform at a prescribed value or more at a diffusion angle of a maximal value or lower of an absolute value of a diffusion angle in a prescribed direction, and which is capable of making the optical intensity 0 at a diffusion angle exceeding the maximal value of the absolute value of the diffusion angle in the prescribed direction.SOLUTION: A diffusion element includes a plurality of shapes obtained according to parallel displacement on at least one xy plane out of a shape represented by z=g(x,y) and a shape represented by z=-g(x,y), where a center of a rectangle with an x-direction side and a y-direction side on an (x,y) plane is an origin, and a smooth function in the rectangle is z=g(x,y). On an xz cross section, an angle formed between a light ray emitted from the diffusion element and a z-axis direction is an absolute value of a diffusion angle on the xz cross section. On a yz cross section, an angle formed between a light ray emitted from the diffusion element and a z-axis direction is an absolute value of a diffusion angle on the yz cross section. In the diffusion element, a desired maximal value of the absolute value of the diffusion angle of the xz cross section, and a desired maximal value of the absolute value of the diffusion angle of the yz cross section can be obtained.SELECTED DRAWING: Figure 17

Description

The present invention relates to a diffusing element that diffuses light emitted from a light source.

In various application fields, a diffusing element that diffuses light emitted from a light source is used (for example, Patent Document 1).

In the diffusing element, in order to control the diffusion angle of the diffused light rays, a diffusing element that combines a plurality of the same shapes, such as a microlens array, may be used. In such a case, if the overall shape of the diffusion element is not smooth, for example, it becomes difficult to process the mold when manufacturing the mold for the diffusion element. Therefore, it is preferable that the overall shape of the diffusion element is smooth.

Further, the intensity of the light diffused by the diffusing element is uniform at the predetermined value or more in the absolute value of the diffusion angle equal to or less than the maximum value of the absolute value of the diffusion angle in the predetermined direction, and the diffusion angle in the predetermined direction. It is desirable that the absolute value of the diffusion angle exceeding the maximum absolute value is 0.

Further, if the convex portion and the concave portion of the diffusing element have the same shape and are arranged at regular intervals, the light rays that have passed through the diffusing element interfere with each other to cause diffraction, and the intensity on the irradiation surface is uniform. It is no longer preferable. Therefore, it is conceivable to disperse the arrangement and shape of the convex portion and the concave portion. However, such processing complicates the design and manufacturing process.

In this way, in the absolute value of the diffusion angle equal to or less than the maximum value of the absolute value of the diffusion angle in the predetermined direction, the light intensity is made uniform above the predetermined value, and the maximum value of the absolute value of the diffusion angle in the predetermined direction is set. A diffuser element has been developed that allows the light intensity to be zero in the absolute value of the diffusion angle that exceeds it, has a smooth shape as a whole, does not cause diffraction, and is easy to design and manufacture. Not.

US6352359B1

Therefore, in the absolute value of the diffusion angle equal to or less than the maximum value of the absolute value of the diffusion angle in the predetermined direction, the light intensity is made uniform above the predetermined value, and the diffusion exceeds the maximum value of the absolute value of the diffusion angle in the predetermined direction. There is a need for a diffusing element which can have the light intensity of 0 in the absolute value of the angle, has a smooth shape as a whole, does not cause diffraction, and has a simple manufacturing process. An object of the present invention is to make the light intensity uniform above a predetermined value at an absolute value of a diffusion angle equal to or less than the maximum value of the absolute value of the diffusion angle in a predetermined direction, and to maximize the absolute value of the diffusion angle in a predetermined direction. In the absolute value of the diffusion angle exceeding the value, the light intensity can be set to 0, the diffusion element has a smooth shape as a whole, does not cause diffraction, and is easy to design and manufacture. To provide.

であり、z=g(x,y)は該矩形内において単一の頂点を有し、該矩形の辺上の任意の点と該頂点とを結ぶ直線に沿って該任意の点から該頂点までｚは単調に増加し、

で表され、

の1階微分が

において連続であり、該頂点のｘ座標において０であり、ｘ座標が該頂点のｘ座標より小さい領域の１階微分が正でｘ座標が該頂点のｘ座標より大きい領域の１階微分が負であり、

の2階微分が、ｘ座標が該頂点のｘ座標より小さい領域及びｘ座標が該頂点のｘ座標より大きい領域においてそれぞれ単一の不連続な点を有し、

の1階微分が

において連続であり、該頂点のｙ座標において０であり、ｙ座標が該頂点のｙ座標より小さい領域の１階微分が正でｙ座標が該頂点のｙ座標より大きい領域の１階微分が負であり、

の2階微分が、ｙ座標が該頂点のｙ座標より小さい領域及びｙ座標が該頂点のｙ座標より大きい領域においてそれぞれ単一の不連続な点を有し、
h₁(x)の２階微分の少なくとも一つの不連続点のｘ座標におけるh₁(x)の１階微分の絶対値がｘｚ断面の拡散角度の絶対値の所望の最大値に対応し、h₂(y)の２階微分の少なくとも一つの不連続点のｙ座標におけるh₂(y)の１階微分の絶対値がｙｚ断面の拡散角度の絶対値の所望の最大値に対応するように定められている。 The diffusion element of the first aspect of the present invention has the center of a rectangle having a side having a length s in the x direction and a side having a length t in the y direction on the (x, y) plane as the origin, and is within the rectangle. Let z = g (x, y) be the smooth function, and on at least one of the xy planes of the shape represented by z = g (x, y) and the shape represented by z = -g (x, y). It has a plurality of shapes obtained by parallel movement, and the angle formed by the light beam emitted from the diffusing element in the xz cross section with respect to the z-axis direction is taken as the absolute value of the diffusing angle of the xz cross section, and in the yz cross section, from the diffusing element. A diffusion element configured such that the angle formed by the emitted light beam in the z-axis direction is the absolute value of the diffusion angle of the yz cross section, and the maximum value of the absolute value of the diffusion angle of the xz cross section and the yz cross section is a desired value. There,
On the sides of the rectangle

Z = g (x, y) has a single vertex in the rectangle, and the vertex from the arbitrary point along the straight line connecting the arbitrary point on the side of the rectangle and the vertex. Z increases monotonically until

Represented by

The first derivative of

Is continuous, 0 in the x-coordinate of the vertex, the first derivative of the region where the x-coordinate is smaller than the x-coordinate of the vertex is positive, and the first-order derivative of the region whose x-coordinate is larger than the x-coordinate of the vertex is negative. And

The second derivative of the above has a single discontinuous point in a region where the x-coordinate is smaller than the x-coordinate of the vertex and in a region where the x-coordinate is larger than the x-coordinate of the vertex.

The first derivative of

Is continuous, 0 in the y-coordinate of the vertex, the first derivative of the region where the y-coordinate is smaller than the y-coordinate of the vertex is positive, and the first-order derivative of the region where the y-coordinate is larger than the y-coordinate of the vertex is negative. And

The second derivative of the above has a single discontinuous point in a region where the y-coordinate is smaller than the y-coordinate of the vertex and in a region where the y-coordinate is larger than the y-coordinate of the vertex.
the absolute value of the first derivative of h ₁ (x) corresponds to the desired maximum value of the absolute value of the diffusion angle of the xz cross section in the second floor x-coordinate of the at least one discontinuity of the derivative of h ₁ (x), as the absolute value of the first derivative of h ₂ (y) in at least one of y coordinate of the point of discontinuity second derivative of h ₂ (y) corresponds to the desired maximum value of the absolute value of the diffusion angle of the yz cross section It is stipulated in.

の形状的な特徴によって、所定の方向の拡散角度の絶対値の最大値以下の拡散角度の絶対値においては光の強度を所定値以上でほぼ一様とし、所定の方向の拡散角度の絶対値の最大値を超える拡散角度の絶対値においては光の強度を０とすることが可能で、全体として滑らかな形状を有し、製造プロセスが簡単である。 The diffusion element according to this aspect is

Due to the shape characteristics of, the light intensity is made almost uniform above the predetermined value at the absolute value of the diffusion angle equal to or less than the maximum value of the absolute value of the diffusion angle in the predetermined direction, and the absolute value of the diffusion angle in the predetermined direction. In the absolute value of the diffusion angle exceeding the maximum value of, the light intensity can be set to 0, the shape is smooth as a whole, and the manufacturing process is simple.

で表され、m及びnは、それぞれx、y方向の矩形の位置を示す整数であり、m及びnの最小値は０であり、mの最大値は該拡散素子のｘ方向の寸法で定まり、ｎの最大値は該拡散素子のｙ方向の寸法で定まる。 The diffusion element according to the first embodiment of the present invention has a shape in which the numbers indicating the positions of the rectangles in the x and y directions are m and n.

Represented by, m and n are integers indicating the positions of rectangles in the x and y directions, respectively, the minimum value of m and n is 0, and the maximum value of m is determined by the dimension of the diffusion element in the x direction. , N is determined by the dimension of the diffusion element in the y direction.

で表され、m及びnは、それぞれx、y方向の矩形の位置を示す整数であり、m及びnの最小値は０であり、mの最大値は該拡散素子のｘ方向の寸法で定まり、ｎの最大値は該拡散素子のｙ方向の寸法で定まる。 The diffusion element according to the second embodiment of the present invention has a shape in which the numbers indicating the positions of the rectangles in the x and y directions are m and n.

Represented by, m and n are integers indicating the positions of rectangles in the x and y directions, respectively, the minimum value of m and n is 0, and the maximum value of m is determined by the dimension of the diffusion element in the x direction. , N is determined by the dimension of the diffusion element in the y direction.

がxの2次以上の関数であり、

によって表され、

がyの2次以上の関数であって、

によって表される。 The diffusion element according to the third embodiment of the present invention is

Is a quadratic or higher function of x

Represented by

Is a quadratic or higher function of y

Represented by.

及び

が偶数次の多項式である。 In the diffusion element according to the fourth embodiment of the present invention

as well as

Is an even-order polynomial.

In the diffusion element according to the fifth embodiment of the present invention, the ratio of the area of the plane on the xy plane to the projected area on the xy plane is 1% or less.

The diffusion element according to the sixth embodiment of the present invention randomly shifts the vertices of each unit figure within a predetermined range with respect to the shape of any of the above diffusion elements, and is a reference. From the unit figure, of f (x, y) corresponding to the second point in the reference unit figure corresponding to any first point in each convex polygon formed by the shifted vertices. It is a diffusion element whose shape is determined by a function whose value is a value corresponding to the first point.

The diffusion element of the present embodiment does not cause diffraction due to the periodic structure, and can make the illuminance distribution on the irradiation surface more uniform.

The diffusion element according to the seventh embodiment of the present invention is a diffusion element obtained by multiplying the z coordinate in each rectangle of any of the above diffusion elements by γ, and the value of γ is 0.9 to 1. It is a diffusion element changed in the range of 1.

The diffusion element of the present embodiment does not cause diffraction due to the periodic structure, and can make the illuminance distribution on the irradiation surface more uniform.

The diffusion element according to the eighth embodiment of the present invention has a shape on a curved surface, and the shape is a projection of the shape on the xy surface of the diffusion element, and the projection projects the xy plane onto the curved surface. Is what you do.

であり、z=g(x,y)は該矩形内において単一の頂点を有し、該矩形の辺上の任意の点と該頂点とを結ぶ直線に沿って該任意の点から該頂点までｚは単調に増加し、

で表され、

の1階微分が

において連続であり、該頂点において０であり、ｘ座標が該頂点のｘ座標より小さい領域の１階微分が正でｘ座標が該頂点のｘ座標より大きい領域の１階微分が負であり、

の2階微分が、ｘ座標が該頂点のｘ座標より小さい領域及びｘ座標が該頂点のｘ座標より大きい領域においてそれぞれ単一の不連続な点を有し、

の1階微分が

において連続であり、該頂点のｙ座標において０であり、ｙ座標が該頂点のｙ座標より小さい領域の１階微分が正でｙ座標が該頂点のｙ座標より大きい領域の１階微分が負であり、

の2階微分が、ｙ座標が該頂点のｙ座標より小さい領域及びｙ座標が該頂点のｙ座標より大きい領域においてそれぞれ単一の不連続な点を有する関数z=g(x,y)を定めるステップと、
ｘｚ断面において、該拡散素子から射出された光線がｚ軸方向となす角度をｘｚ断面の拡散角度の絶対値とし、ｙｚ断面において、該拡散素子から射出された光線がｚ軸方向となす角度をｙｚ断面の拡散角度の絶対値として、h₁(x)の２階微分の少なくとも一つの不連続点のｘ座標におけるh₁(x)の１階微分の絶対値がｘｚ断面の拡散角度の絶対値の所望の最大値に対応し、h₂(y)の２階微分の少なくとも一つの不連続点のｙ座標におけるh₂(y)の１階微分の絶対値がｙｚ断面の拡散角度の絶対値の所望の最大値に対応するようにh₁(x)及びh₂(y)の係数を調整するステップと、
z=g(x,y)で表される形状及びz=-g(x,y) で表される形状のそれぞれのxy平面上の平行移動によって全体の形状を定めるステップと、を含む。 In the method for manufacturing a diffuser element according to the second aspect of the present invention, the origin is the center of a rectangle having a side having a length s in the x direction and a side having a length t in the y direction on the (x, y) plane. Let z = g (x, y) be the smooth function in the rectangle, and at least one xy of the shape represented by z = g (x, y) and the shape represented by z = -g (x, y). A method for manufacturing a diffuser element having a plurality of shapes obtained by translation on a plane.
On the sides of the rectangle

Z = g (x, y) has a single vertex in the rectangle, and the vertex from the arbitrary point along the straight line connecting the arbitrary point on the side of the rectangle and the vertex. Z increases monotonically until

Represented by

The first derivative of

Is continuous, is 0 at the vertex, the first derivative of the region whose x-coordinate is smaller than the x-coordinate of the vertex is positive, and the first derivative of the region whose x-coordinate is larger than the x-coordinate of the vertex is negative.

The second derivative of the above has a single discontinuous point in a region where the x-coordinate is smaller than the x-coordinate of the vertex and in a region where the x-coordinate is larger than the x-coordinate of the vertex.

The first derivative of

Is continuous, 0 in the y-coordinate of the vertex, the first derivative of the region where the y-coordinate is smaller than the y-coordinate of the vertex is positive, and the first-order derivative of the region where the y-coordinate is larger than the y-coordinate of the vertex is negative. And

The second derivative of z = g (x, y) has a single discontinuous point in the region where the y-coordinate is smaller than the y-coordinate of the vertex and in the region where the y-coordinate is larger than the y-coordinate of the vertex. Steps to determine and
In the xz cross section, the angle formed by the light beam emitted from the diffusing element in the z-axis direction is defined as the absolute value of the diffusion angle in the xz cross section, and in the yz cross section, the angle formed by the light beam emitted from the diffusing element in the z-axis direction is defined as the absolute value. As the absolute value of the diffusion angle of the yz cross section, the absolute value of the _first derivative of h 1 (x) at the x coordinate of at least one discontinuity of the second derivative of h ₁ (x) is the absolute value of the diffusion angle of the xz cross section. corresponding to the desired maximum value, h ₂ 2 floor absolute value of the first derivative of h ₂ (y) in the y-coordinate of the at least one discontinuity of the differential absolute diffusion angle yz cross section of the (y) Steps to adjust the derivatives _{of h 1} (x) and h ₂ (y) to correspond to the desired maximum value, and
It includes a step of defining the overall shape by translation on each xy plane of the shape represented by z = g (x, y) and the shape represented by z = -g (x, y).

According to the method for manufacturing a diffusing element of this embodiment, the intensity of light diffused by the diffusing element is made substantially uniform at an absolute value of a diffusing angle equal to or less than the maximum value of the absolute value of the diffusing angle in a predetermined direction. At an absolute value of the diffusion angle exceeding the maximum value of the absolute value of the diffusion angle in a predetermined direction, a diffusion element having the intensity of light diffused by the diffusion element of 0 can be obtained.

It is a figure for demonstrating the shape of the diffusion element of one Embodiment of this invention. It is a figure which shows the shape of h ₁ (x) and h _{2 (y).} It is a figure for demonstrating the whole shape z = f (x, y). It is a figure which shows z = f (x, 0) and z = f (0, y) corresponding to the convex part in the whole shape z = f (x, y). It is a figure which shows z = f (x, 0.8) and z = f (0.4, y) corresponding to the concave part in the whole shape z = f (x, y). It is a flow chart which shows the method which disperses the space between adjacent convex part or adjacent concave part. It is a figure which shows the lattice point on the xy plane, and the predetermined range which moves the lattice point. It is a figure which shows the position of the point corresponding to each grid point after moving each grid point. It is a figure which shows the convex quadrangle formed by the point after moving. It is a figure which shows the convex quadrangle and the original rectangle formed by the point after moving. It is a figure which shows the intensity distribution of the light obtained by injecting parallel light into the diffusing element which has the shape of z = f (x, y) which does not disperse the position and height of a lattice point. It is a figure which shows the intensity distribution of the light obtained by injecting parallel light into the diffusing element which has the shape of z = f ″ (x, y) which dispersed the position and height of a lattice point. It is a figure for demonstrating the diffusion angle of the light ray diffused by a diffusing element. It is a figure for demonstrating the relationship between the shape of a diffusion element, and a diffusion angle. It is a top view of the diffusion element of Example 1. FIG. It is an xz cross-sectional view corresponding to the straight line A and the straight line B of FIG. 15 of the diffusion element of Example 1. FIG. It is a figure which shows the shape _{of h 1} (x) of the diffusion element of Example 1. FIG. It is a figure which shows the 1st derivative of the shape shown in FIG. It is a figure which shows the 2nd derivative of the shape shown in FIG. It is a figure which shows the intensity distribution in the xz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 1 has passed through a diffusing element. It is a figure which shows the intensity distribution in the yz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 1 has passed through a diffusing element. It is a top view of the diffusion element of Example 2. FIG. It is an xz cross-sectional view corresponding to the straight line A and the straight line B of FIG. 22 of the diffusion element of Example 2. FIG. It is a figure which shows the 1st derivative of the shape shown in FIG. It is a figure which shows the 2nd derivative of the shape shown in FIG. It is a figure which shows the intensity distribution in the xz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 2 has passed through a diffusing element. It is a figure which shows the intensity distribution in the xz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 2 has passed through a diffusing element. It is a figure which shows the intensity distribution in the yz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 2 has passed through a diffusing element. It is a figure which shows the intensity distribution in the yz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 2 has passed through a diffusing element. It is a figure which shows the shape _{of h 1} (x) of the diffusion element of Example 3. It is a figure which shows the 1st derivative of the shape shown in FIG. 28. It is a figure which shows the 2nd derivative of the shape shown in FIG. 28. It is a figure which shows the intensity distribution in the xz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 3 has passed through a diffusing element. It is a figure which shows the intensity distribution in the xz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 3 has passed through a diffusing element. It is a figure which shows the intensity distribution in the yz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 3 has passed through a diffusing element. It is a figure which shows the intensity distribution in the yz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 3 has passed through a diffusing element. It is a figure which shows the shape _{of h 1} (x) of the diffusion element of Example 4. The cross section of FIG. 33 is an xz cross section. It is a figure which shows the 1st derivative of the shape shown in FIG. 33. It is a figure which shows the 2nd derivative of the shape shown in FIG. 33. It is a figure which shows the intensity distribution in the xz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 4 passes through a diffusing element. It is a figure which shows the intensity distribution in the yz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of Example 4 passes through a diffusing element. It is a figure which shows the intensity distribution in the xz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of the modification of Example 4 passes through a diffusing element. It is a figure which shows the intensity distribution in the yz cross section after the parallel light incident perpendicular to the xy plane of the diffusing element of the modification of Example 4 passes through a diffusing element. It is a flow chart which shows the manufacturing method of the diffusion element by this invention.

をその境界、すなわち基準の矩形の辺とすると、以下の関係が成立する。

のとき

のとき

FIG. 1 is a diagram for explaining the shape of the diffusion element according to the embodiment of the present invention. On the (x, y) plane, a rectangular grid with an interval s in the x direction and an interval t in the y direction is defined. Let one of the rectangles having the length s of the side in the x direction and the length t of the side in the y direction be the reference rectangle. The position of the rectangle in the x direction is represented by the integer m, and the position in the y direction is represented by the integer n. The minimum values of m and n are 0, the maximum value of m is determined by the dimension of the diffusion element in the x direction, and the maximum value of n is determined by the dimension of the diffusion element in the y direction. The reference rectangle is represented by m = 0 and n = 0. The shape of the reference rectangle is represented by g (x, y). The origin of the (x, y) coordinates is the center of the reference rectangle. Area within a rectangle relative to S,

Let be the boundary, that is, the side of the reference rectangle, and the following relationship holds.

When

When

で表され、

の1階微分が

において連続であり、該頂点のｘ座標において０であり、ｘ座標が該頂点のｘ座標より小さい領域の１階微分が正でｘ座標が該頂点のｘ座標より大きい領域の１階微分が負であり、

の2階微分が、ｘ座標が該頂点のｘ座標より小さい領域及びｘ座標が該頂点のｘ座標より大きい領域においてそれぞれ単一の不連続な点を有し、

の1階微分が

において連続であり、該頂点のｙ座標において０であり、ｙ座標が該頂点のｙ座標より小さい領域の１階微分が正でｙ座標が該頂点のｙ座標より大きい領域の１階微分が負であり、

の2階微分が、ｙ座標が該頂点のｙ座標より小さい領域及びｙ座標が該頂点のｙ座標より大きい領域においてそれぞれ単一の不連続な点を有する。 The shape represented by z = g (x, y) has a single vertex within the rectangle, from any point along the straight line connecting the apex to any point on the side of the rectangle. Z monotonically increases to the apex,

Represented by

The first derivative of

Is continuous, 0 in the x-coordinate of the vertex, the first derivative of the region where the x-coordinate is smaller than the x-coordinate of the vertex is positive, and the first-order derivative of the region whose x-coordinate is larger than the x-coordinate of the vertex is negative. And

The second derivative of the above has a single discontinuous point in a region where the x-coordinate is smaller than the x-coordinate of the vertex and in a region where the x-coordinate is larger than the x-coordinate of the vertex.

The first derivative of

Is continuous, 0 in the y-coordinate of the vertex, the first derivative of the region where the y-coordinate is smaller than the y-coordinate of the vertex is positive, and the first-order derivative of the region where the y-coordinate is larger than the y-coordinate of the vertex is negative. And

The second derivative of the above has a single discontinuous point in a region where the y-coordinate is smaller than the y-coordinate of the vertex and in a region where the y-coordinate is larger than the y-coordinate of the vertex.

z = g (x, y) is a smooth function over the entire region. Further, it is preferable that the X-axis and the y-axis passing through the center of the region are symmetric, the extremum is one, and the x and y coordinates of the extremum match the x and y coordinates of the center of the region.

Assuming that the overall shape of the diffusing element is z = f (x, y), z = f (x, y) can be expressed by the following equation.

及び各格子点に配置したg(x,y)の符号を反転させた形状

を組み合わせた形状である。このように、互いに符号の異なる同一の形状を組み合わせた形状を使用するのは、拡散角の比較的大きな形状の領域を増加させることによって、拡散された光による照射面における強度をより一様にするためである。全体の形状z=f(x,y)は、滑らかな関数である。 The overall shape z = f (x, y) is the same shape as g (x, y) placed in the center of each rectangle of the grid.

And the shape in which the sign of g (x, y) placed at each grid point is inverted.

It is a combination of. In this way, the use of shapes that combine the same shapes with different signs makes the intensity on the irradiated surface by the diffused light more uniform by increasing the region of the shape with a relatively large diffusion angle. To do. The overall shape z = f (x, y) is a smooth function.

If the overall shape of the diffusing element is smooth, for example, when manufacturing a mold for the diffusing element, the processing of the mold becomes easy.

上記の式において、

はxが(a,b)の範囲に属することを表し、

はxが(a,b)の範囲に属さないことを表す。 The following functions may be adopted as g (x, y).

In the above formula

Indicates that x belongs to the range (a, b)

Indicates that x does not belong to the range (a, b).

FIG. 2 is a diagram showing the shapes of _{h 1} (x) and h _{2 (y).} The horizontal axis of FIG. 2 represents the x-axis or the y-axis, and the vertical axis of FIG. 2 represents h ₁ (x) or h ₂ (y). The shapes of h ₁ (x) and h ₂ (y) are defined so that the intensity on the surface irradiated by the diffused light is as uniform as possible.

FIG. 3 is a diagram for explaining the overall shape z = f (x, y). In FIG. 3, the grid points are indicated by black dots, and the center of the rectangle is indicated by white dots. The origin (0,0) is the center of the reference rectangle.

In FIG. 3, the portion corresponding to the side of the rhombus shown by the dotted line is z = 0. Of the rhombuses surrounded by the dotted lines, convex portions are formed in the regions including white dots, and concave portions are formed in the regions including black dots.

FIG. 4 is a diagram showing z = f (x, 0) and z = f (0, y) corresponding to the convex portion of the overall shape z = f (x, y). The horizontal axis of FIG. 4 represents the x-axis coordinate or the y-axis coordinate, and the vertical axis of FIG. 4 represents the z-axis coordinate.

FIG. 5 is a diagram showing z = f (x, 0.8) and z = f (0.4, y) corresponding to the concave portion in the overall shape z = f (x, y). The horizontal axis of FIG. 5 represents the x-axis coordinate or the y-axis coordinate with the origin at (0.4, 0.8), and the vertical axis coordinate of FIG. 5 represents z.

By the way, if the convex portion and the concave portion of the diffusing element have the same shape and are arranged at regular intervals, the light rays that have passed through the diffusing element interfere with each other to cause diffraction, and the intensity on the irradiation surface is uniform. It is no longer preferable. Therefore, in order to make the intensity on the irradiated surface by the diffused light as uniform as possible, the distance between the adjacent convex portions or the adjacent concave portions, or the height of the convex portion or the concave portion is set. It is possible to disperse.

FIG. 6 is a flow chart showing a method of varying the spacing between adjacent convex portions or adjacent concave portions.

7 to 10 are views for explaining a method of varying the spacing between adjacent convex portions or adjacent concave portions shown in FIG.

In step S1010 of FIG. 6, each grid point on the xy plane is randomly moved within a predetermined range.

FIG. 7 is a diagram showing grid points on the xy plane and a predetermined range for moving the grid points. The predetermined range is, for example, an ellipse in which the length of the axis in the x-axis direction is α · s and the length in the y-axis direction is β · t. The values of α and β are preferably in the range of 0.1 to 0.4. Each grid point is moved within the ellipse corresponding to the grid point. Move each grid point so that the relative positions in the ellipse of the grid points after moving are evenly distributed in the ellipse. In general, the range for moving each grid point may be a predetermined range around each grid point. That is, each grid point may be moved so that the relative positions of the grid points after the movement within the predetermined range are uniformly distributed in the predetermined range.

FIG. 8 is a diagram showing the positions of the points corresponding to the respective grid points after moving the respective grid points.

In step S1020 of FIG. 6, the projection matrix from the original rectangle to the convex quadrangle formed by the grid points after being moved is obtained. Here, the predetermined range around each of the above grid points needs to be defined so that the figure formed by the grid points after being moved becomes a convex quadrangle (generally, a convex polygon). ..

FIG. 9 is a diagram showing a convex quadrangle formed by points after being moved. The coordinates (X1, Y1), (X2, Y2), (X3, Y3) and (X4, Y4) of the vertices of the convex quadrangle are the origins of the coordinates corresponding to the lower left vertices of the vertices of the rectangle before moving. Defined as (0,0).

FIG. 10 is a diagram showing a convex quadrangle formed by points after being moved and a rectangle obtained by normalizing the original rectangle. As an example, the standardized rectangle is a square in which the lower left vertex is located at the origin and the side lengths in the x-axis direction and the y-axis direction are 1.

A13 = X1
A23 = Y1
A31 = {(X4-X3)*(Y1-Y2)-(Y4-Y3)*(X1-X2)}/{(Y4-Y3)*(X4-X2)-(X4-X3)*(Y4-Y2)}
A32 = {(X4-X2)*(Y1-Y3)-(Y4-Y2)*(X1-X3)}/{(Y4-Y2)*(X4-X3)-(X4-X2)*(Y4-Y3)}
A11 = (A31+1)*X2-X1
A12 = (A32+1)*X3-X1
A21 = (A31+1)*Y2-Y1
A22 = (A32+1)*Y3-Y1
A33 = 1
An example of the projection matrix A from the normalized rectangle to the convex quadrangle formed by the grid points after being moved is as follows.

A13 = X1
A23 = Y1
A31 = {(X4-X3) * (Y1-Y2)-(Y4-Y3) * (X1-X2)} / {(Y4-Y3) * (X4-X2)-(X4-X3) * (Y4-Y4- Y2)}
A32 = {(X4-X2) * (Y1-Y3)-(Y4-Y2) * (X1-X3)} / {(Y4-Y2) * (X4-X3)-(X4-X2) * (Y4-Y4- Y3)}
A11 = (A31 + 1) * X2-X1
A12 = (A32 + 1) * X3-X1
A21 = (A31 + 1) * Y2-Y1
A22 = (A32 + 1) * Y3-Y1
A33 = 1

The projection matrix A projects any point (X', Y') in the normalized rectangle onto any point (X, Y) in the convex quadrangle.

The vertices of the normalized rectangle are, for example, by the projection matrix A above.
X'= 0, Y'= 0 means X = X1, Y = Y1,
X'= 1, Y'= 0 means X = X2, Y = Y2
Projected to.

In step S1030 of FIG. 6, the inverse matrix A ^-1 of the projection matrix A is obtained.

In step S1040 of FIG. 6, the inverse matrix A ^-1 sets the second point (X', Y') in the normalized rectangle corresponding to any first point (X, Y) in the convex quadrangle. Ask.

In step S1050 of FIG. 6, the value of the normalized function f'(x, y) corresponding to the second point (X', Y') is obtained. Here, the normalization function f'(x, y) is the region of x: (-0.3,0.3), y: (-0.6,0.6) of f (x, y) x: (0,1). , y: A function standardized to (0,1).

In step S1060 of FIG. 6, the value of the normalization function f'(x, y) corresponding to the second point (X', Y') is set to the value corresponding to the first point (X, Y). Find the function f'' (x, y). The function f ″ (x, y) is as smooth as the function f (x, y).

In the above, a rectangle standardized from the original rectangle was used to obtain the value of the function f ″ (x, y) corresponding to the points of the convex quadrangle formed by the points after the movement. As another embodiment, the original rectangle may be used as it is.

In step S1070 of FIG. 6, by the function z = f''(x, y), the coordinates of the vertices are (X1, Y1), (X2, Y2), (X3, Y3) and (X4, Y4). Determine the shape of the diffuser corresponding to the quadrangle. A diffusion element having a smooth shape can be obtained even if a plurality of rectangles having the same shape are transformed into convex quadrangles having various shapes by varying the positions of the lattice points.

In step S1080 of FIG. 6, the height of the shape corresponding to each convex quadrangle is randomly varied. The height of the shape is preferably such that the value of the function z = f ″ (x, y) can be uniformly varied in the range of 0.9 to 1.1 times.

By defining the shape as described above, the influence of diffraction due to the periodic structure can be reduced, and the intensity on the irradiated surface by the diffused light can be made more uniform.

FIG. 11 shows the intensity of light obtained by injecting parallel light perpendicular to the xy plane onto a diffusing element having a shape of z = f (x, y) in which the positions and heights of the lattice points are not dispersed. It is a figure which shows the distribution. The diffusion angle in the xz cross section is ± 6 degrees, and the diffusion angle in the yz cross section is ± 4.4 degrees.

FIG. 12 shows the light obtained by injecting parallel light perpendicular to the xy plane onto a diffusing element having the shape of z = f''(x, y) with varying positions and heights of the lattice points. It is a figure which shows the intensity distribution. The diffusion angle in the xz cross section is ± 6 degrees, and the diffusion angle in the yz cross section is ± 4.4 degrees.

In FIGS. 11 and 12, the intensity of light and the illuminance on the irradiated surface are represented by shading, and the white portion has high illuminance. Comparing FIGS. 11 and 12, the illuminance distribution in FIG. 12 is more uniform than the illuminance distribution in FIG.

上記の関係から、以下の式が導かれる。

ここで、ｌを、たとえば図４における凸の部分の長さの四分の一の長さとし、Ｒを曲率半径の平均値として、これらの値を上記の式に代入すると拡散角が求まる。このように、拡散角は拡散素子の形状によって定まる。 FIG. 13 is a diagram for explaining the diffusion angle of the light rays diffused by the diffusion element. It is assumed that the light traveling in the z-axis direction described with reference to FIGS. 4 and 5 is diffused in the diffusing element. The distance from the point through which the light ray passes on the surface of the diffusing element to the z-axis is l, the angle of incidence of the light ray on the surface and the angle of emission from the surface are θ ₁ and θ ₂ , respectively, and the material of the diffusing element is Let n be the refractive index of, and let R be the radius of curvature of the surface at that point. Assuming that the diffusion angle, that is, the angle formed by the light rays passing through the diffusion element with the z-axis is θ, the following relationship is established when _{θ 1} and θ _{2 are sufficiently small.}

From the above relationship, the following equation is derived.

Here, l is, for example, a quarter of the length of the convex portion in FIG. 4, R is the average value of the radius of curvature, and these values are substituted into the above equation to obtain the diffusion angle. In this way, the diffusion angle is determined by the shape of the diffusion element.

をその境界、すなわち単位図形の辺として、以下の関係を満たす。

のとき

のとき

The diffusion element of the above embodiment has a shape based on a rectangular grid. As another embodiment, instead of the rectangular lattice, a planar lattice including a rhombic lattice, a hexagonal lattice, a square lattice, and a parallel lattice may be used. In that case, the function z = g (x, y) is a shape that includes a symmetric and smooth shape with respect to the x-axis and y-axis, with the center of the unit figure that constitutes the plane grid such as a rhombus and a regular hexagon as the origin. May be good. Further, the shape may have a single extremum on the z-axis. The shape has S as a region within the unit figure.

Is the boundary, that is, the side of the unit figure, and the following relationship is satisfied.

When

When

該任意の単位図形に隣接する単位図形の中心の座標を

で表すと、

で表せる形状が得られる。 Also in the case of this embodiment, as in the case of the rectangular lattice embodiment, the overall shape of the diffusion element is z = f (x, y), and the coordinates of the center of an arbitrary unit figure are set.

The coordinates of the center of the unit figure adjacent to the arbitrary unit figure

Expressed in

A shape that can be represented by is obtained.

Further, as in the case of the rectangular grid, the unit figure is deformed by scattering the grid points within a predetermined range, and the function f''(x, y) is obtained for the deformed unit figure, and the function f'(x, y) is obtained. The shape of the diffuser element corresponding to the deformed unit figure can be determined by'(x, y). Further, the height of the shape corresponding to the unit figure can be randomly varied.

In this way, even when a rhombic lattice, a hexagonal lattice, a square lattice, or a parallelepiped lattice is used instead of the rectangular lattice, the influence of diffraction due to the periodic structure is reduced, and the irradiated surface by the diffused light is used. The strength in can be made more uniform.

Further, a lattice shape may be formed on a curved surface including a spherical surface and an aspherical surface. In that case, the present invention can be applied by projecting a planar grid onto a curved surface.

The relationship between the shape of the diffusion element and the diffusion angle will be further described. The diffusion angle is formed by a reference plane of the diffusion element, that is, a plane perpendicular to the x and y planes, for example, a straight line perpendicular to the xy plane in the xz plane, for example, the z-axis and the light beam after passing through the diffusion element. The angle (acute angle).

さらに、スネルの法則から光線が該面を通過する点において以下の関係が成立する。

式（１）においてｎは拡散素子の材料の屈折率を示す。式（１）によれば、ｘｙ平面に垂直な光線が拡散素子の凸部の頂点を通過する場合に光線の入射角θin及び接線角φが０度であり拡散角度θも０度となる。断面形状が滑らかな場合に拡散角度θの絶対値は接線角φにしたがって増加し、接線角φが最大の時に最大となると考えられる。他方、接線角φの正接の絶対値は、拡散素子のｘｚ断面形状を示す曲線ｚ＝ｆ（ｘ）の一階微分の絶対値に等しく以下のように表される。

このように、拡散素子のxz断面における拡散角度の絶対値の最大値は、拡散素子のxz断面の接線角の絶対値の最大値、すなわち拡散素子の断面形状を示す曲線の一階微分の絶対値の最大値によって定まる。 FIG. 14 is a diagram for explaining the relationship between the shape of the diffusion element and the diffusion angle. FIG. 14 shows the xz cross section of the diffusing element. The arrow in FIG. 14 indicates the traveling direction of the light ray. The light beam travels perpendicular to the xy plane and enters the diffusing element. θin represents the angle of incidence of the light beam on the surface of the convex portion of the diffusing element, and θout represents the angle of emission of the light ray from the above-mentioned surface. θ represents the diffusion angle. In FIG. 14, the absolute value of the angle formed by the tangent line and the x-axis at a point on the curve representing the surface of the diffusing element is referred to as a tangent line angle φ. From the definition of the tangent angle, the following relationship holds at the point where the light ray passes through the surface.

Further, according to Snell's law, the following relationship is established at the point where a light ray passes through the surface.

In the formula (1), n represents the refractive index of the material of the diffusing element. According to the equation (1), when a light ray perpendicular to the xy plane passes through the apex of the convex portion of the diffusion element, the incident angle θin and the tangent angle φ of the light ray are 0 degrees, and the diffusion angle θ is also 0 degrees. When the cross-sectional shape is smooth, the absolute value of the diffusion angle θ increases according to the tangent angle φ, and it is considered that the absolute value becomes maximum when the tangent angle φ is maximum. On the other hand, the absolute value of the tangent of the tangent angle φ is equal to the absolute value of the first derivative of the curve z = f (x) indicating the xz cross-sectional shape of the diffusing element and is expressed as follows.

In this way, the maximum value of the absolute value of the diffusion angle in the xz cross section of the diffuser is the maximum value of the absolute value of the tangential angle of the xz cross section of the diffuser, that is, the absolute value of the first derivative of the curve indicating the cross section shape of the diffuser Determined by the maximum value.

Other examples of the present invention will be described below. The shape of the reference rectangle of the embodiment is expressed by the following equation. The length of the side of the reference rectangle in the x-axis direction is s millimeter, and the length of the side in the y-axis direction is t millimeter.

Example 1
In the first embodiment, all but A _{2 of A i of h 1} (x) are 0, and all but B _{2 of B i of h 2} (y) are 0. _{H 1} (x) and h ₂ (y) are defined with the maximum and minimum values of the diffusion angle of the xz cross section being ± 9 degrees and the maximum and minimum values of the diffusion angle of the yz cross section being ± 7 degrees, and the coefficients are as follows. That's right.
s = 0.3, A ₁ = 0, A ₂ = 10, A ₃ = 0, 4th and subsequent coefficients = 0
t = 0.4, B ₁ = 0, B ₂ = 10, B ₃ = 0, 4th and subsequent coefficients = 0
h ₁ (x) and h ₂ (y) are expressed as follows.

The shape f (x, y) of the diffusion element of the first embodiment is a combination of a convex shape g (x, y) and a concave shape-g (x, y), and is expressed by the following equation. To.

FIG. 15 is a plan view of the diffusion element of the first embodiment.

FIG. 16 is an xz cross-sectional view of the diffusion element of Example 1 corresponding to a straight line equidistant and parallel to the two straight lines shown by A in FIG. 15 and a straight line equidistant and parallel to the two straight lines shown by B. Is. The horizontal axis of FIG. 16 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 16 indicates the z coordinate, and the unit is millimeter.

FIG. 17 is a diagram showing the shape _{of h 1} (x) of the diffusion element of the first embodiment. The cross section of FIG. 17 is an xz cross section. The horizontal axis of FIG. 17 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 17 shows the z coordinate, and the unit is millimeter.

の最大値は０．３である。したがって、式（２）から接線角φの最大値は１６．７度である。この値及びn=1.5を式（１）に代入すると、拡散角度の最大値θは約９度となる。 FIG. 18 is a diagram showing the first derivative of the shape shown in FIG. The horizontal axis of FIG. 18 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 18 shows the first derivative value of z, and the unit is a dimensionless number. Absolute value of first derivative from FIG.

The maximum value of is 0.3. Therefore, from the equation (2), the maximum value of the tangent angle φ is 16.7 degrees. Substituting this value and n = 1.5 into Eq. (1), the maximum value θ of the diffusion angle is about 9 degrees.

FIG. 19 is a diagram showing the second derivative of the shape shown in FIG. The horizontal axis of FIG. 19 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 19 shows the second derivative value of z, and the unit is the reciprocal of the millimeter.

FIG. 20 is a diagram showing the intensity distribution in the xz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 1 has passed through the diffusing element. The horizontal axis of 20 in the figure indicates the diffusion angle in the xz cross section, and the unit is degrees. The vertical axis of FIG. 20 shows the intensity of light in the xz cross section, and the unit is an arbitrary unit representing the relative intensity in Example 1. According to FIG. 20, the maximum diffusion angle is about ± 9 degrees, and the shape of the intensity distribution shows a steep near this angle.

FIG. 21 is a diagram showing the intensity distribution in the yz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 1 has passed through the diffusing element. The horizontal axis of 21 in the figure indicates the diffusion angle in the yz cross section, and the unit is degrees. The vertical axis of FIG. 21 shows the intensity distribution in the yz cross section of light, and the unit is an arbitrary unit representing the relative intensity in Example 1. According to FIG. 21, the maximum diffusion angle is about ± 7 degrees, and the shape of the intensity distribution shows a steep near this angle.

According to FIGS. 20 and 21, the shape of the light intensity distribution by the diffusion element of the first embodiment is 0 when the absolute value of the diffusion angle is larger than the maximum value, and is uniform when the absolute value is equal to or less than the maximum value. It is a shape close to an ideal rectangular shape.

Example 2
The g (x, y) of Example 2 is the same as the g (x, y) of Example 1. The shape f (x, y) of the diffusion element of the second embodiment is a shape in which only the convex shape g (x, y) is combined, and is represented by the following equation.

FIG. 22 is a plan view of the diffusion element of the second embodiment.

FIG. 23 is an xz cross-sectional view of the diffusion element of the second embodiment corresponding to a straight line equidistant and parallel to the two straight lines shown by A in FIG. 22 and a straight line equidistant and parallel to the two straight lines shown by B. Is. The horizontal axis of FIG. 23 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 23 shows the z coordinate, and the unit is millimeter.

FIG. 24 is a diagram showing the first derivative of the shape shown in FIG. 23. The horizontal axis of FIG. 24 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 24 shows the first derivative value of z, and the unit is a dimensionless number.

FIG. 25 is a diagram showing the second derivative of the shape shown in FIG. 23. The horizontal axis of FIG. 25 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 25 shows the second derivative value of z, and the unit is the reciprocal of the millimeter.

FIG. 26A is a diagram showing the intensity distribution in the xz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 2 has passed through the diffusing element. The horizontal axis of 26A in the figure indicates the diffusion angle in the xz cross section, and the unit is degrees. The vertical axis of FIG. 26A shows the intensity distribution in the xz cross section of light, and the unit is an arbitrary unit representing the relative intensity in Example 2.

FIG. 26B is a diagram showing the intensity distribution in the xz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 2 has passed through the diffusing element. The horizontal axis of 26B in the figure indicates the diffusion angle in the xz cross section, and the unit is degrees. The vertical axis of FIG. 26B shows the intensity distribution in the xz cross section of light on a logarithmic scale, and the unit is an arbitrary unit representing the relative intensity in Example 2. According to FIG. 26B, the maximum diffusion angle is about ± 9 degrees, and the shape of the intensity distribution shows a steep near this angle.

FIG. 27A is a diagram showing the intensity distribution in the yz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 2 has passed through the diffusing element. The horizontal axis of 27A in the figure indicates the diffusion angle in the yz cross section, and the unit is degrees. The vertical axis of FIG. 27A shows the intensity distribution in the yz cross section of light, and the unit is an arbitrary unit representing the relative intensity in Example 2.

FIG. 27B is a diagram showing the intensity distribution in the yz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 2 has passed through the diffusing element. The horizontal axis of 27B in the figure indicates the diffusion angle in the yz cross section, and the unit is degrees. The vertical axis of FIG. 27B shows the intensity distribution in the yz cross section of light on a logarithmic scale, and the unit is an arbitrary unit representing the relative intensity in Example 2. According to FIG. 27B, the maximum diffusion angle is about ± 7 degrees, and the shape of the intensity distribution shows a steep near this angle.

In FIGS. 26A, 26B, 27A, and 27B, the reason why the light intensity corresponding to the diffusion angle of 0 degrees is higher than that in the cases of FIGS. 20 and 21, is that the portion of the shape of Example 2 parallel to the xy plane. It is considered that this is because the area of is larger than the area of the portion of the shape of Example 1 parallel to the xy plane.

Example 3
In the third embodiment, all but A _{3 of A i of h 1} (x) are 0, and all but B _{3 of B i of h 2} (y) are 0. The maximum and minimum values of the diffusion angle in the xz cross section are designed to be ± 10 degrees, and the maximum and minimum values of the diffusion angle in the yz cross section are designed to be ± 5 degrees, and the coefficients are as follows.
s = 0.3, A ₁ = 0, A ₂ = 0, A ₃ = 55, 4th and subsequent coefficients = 0
t = 0.6, B ₁ = 0, B ₂ = 0, B ₃ = 55, 4th and subsequent coefficients = 0

The shape f (x, y) of the diffusion element of the third embodiment is a combination of a convex shape g (x, y) and a concave shape-g (x, y), and is expressed by the following equation. To.

FIG. 28 is a diagram showing the shape _{of h 1} (x) of the diffusion element of the third embodiment. The cross section of FIG. 28 is an xz cross section. The horizontal axis of FIG. 28 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 28 indicates the z coordinate, and the unit is millimeter.

FIG. 29 is a diagram showing the first derivative of the shape shown in FIG. 28. The horizontal axis of FIG. 29 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 29 shows the first derivative value of z, and the unit is a dimensionless number.

FIG. 30 is a diagram showing the second derivative of the shape shown in FIG. 28. The horizontal axis of FIG. 30 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 30 shows the second derivative value of z, and the unit is the reciprocal of the millimeter.

FIG. 31A is a diagram showing the intensity distribution in the xz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 3 has passed through the diffusing element. The horizontal axis of 31A in the figure indicates the diffusion angle in the xz cross section, and the unit is degrees. The vertical axis of FIG. 31A shows the intensity distribution in the xz cross section of light, and the unit is an arbitrary unit representing the relative intensity in Example 3.

FIG. 31B is a diagram showing the intensity distribution in the xz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 3 has passed through the diffusing element. The horizontal axis of 31B in the figure indicates the diffusion angle in the xz cross section, and the unit is degrees. The vertical axis of FIG. 31B shows the intensity distribution in the xz cross section of light on a logarithmic scale, and the unit is an arbitrary unit representing the relative intensity in Example 3. According to FIG. 31B, the maximum diffusion angle is about ± 10 degrees, and the shape of the intensity distribution shows a steep near this angle.

FIG. 32A is a diagram showing the intensity distribution in the yz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 3 has passed through the diffusing element. The horizontal axis of 32A in the figure indicates the diffusion angle in the yz cross section, and the unit is degrees. The vertical axis of FIG. 32A shows the intensity distribution in the yz cross section of light, and the unit is an arbitrary unit representing the relative intensity in Example 3.

FIG. 32B is a diagram showing the intensity distribution of the light passing through the diffusing element of Example 3 in the yz cross section. The horizontal axis of 32B in the figure indicates the diffusion angle in the yz cross section, and the unit is degrees. The vertical axis of FIG. 32B shows the intensity distribution in the yz cross section of light on a logarithmic scale, and the unit is an arbitrary unit representing the relative intensity in Example 3. According to FIG. 32B, the maximum diffusion angle is about ± 5 degrees, and the shape of the intensity distribution shows a steep near this angle.

Example 4
In Example 4, h ₁ (x) A _i other than A ₂ and A ₄ is 0, and h ₂ (y) B _i other than B ₂ and B ₄ is 0. The maximum and minimum values of the diffusion angle in the xz cross section are designed to be ± 20 degrees, and the maximum and minimum values of the diffusion angle in the yz cross section are designed to be ± 10 degrees, and the coefficients are as follows.
s = 0.6, A ₂ = -3.6, A ₄ = -0.5
t = 1.2, B ₂ = -3.6, B ₄ = -0.5
A _i and B _i are 0 when i is 5 or more.

The shape f (x, y) of the diffusion element of the fourth embodiment is a combination of a convex shape g (x, y) and a concave shape-g (x, y), and is expressed by the following equation. To.

FIG. 33 is a diagram showing the shape _{of h 1} (x) of the diffusion element of the fourth embodiment. The cross section of FIG. 33 is an xz cross section. The horizontal axis of FIG. 33 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 33 indicates the z coordinate, and the unit is millimeter.

の最大値は０．７である。 FIG. 34 is a diagram showing the first derivative of the shape shown in FIG. 33. The horizontal axis of FIG. 34 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 34 shows the first derivative value of z, and the unit is a dimensionless number. Absolute value of first derivative from Fig. 34

The maximum value of is 0.7.

FIG. 35 is a diagram showing the second derivative of the shape shown in FIG. 33. The horizontal axis of FIG. 35 indicates the x-coordinate, and the unit is millimeter. The vertical axis of FIG. 35 shows the second derivative value of z, and the unit is the reciprocal of the millimeter.

FIG. 36 is a diagram showing the intensity distribution in the xz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 4 has passed through the diffusing element. The horizontal axis of 36 in the figure indicates the diffusion angle in the xz cross section, and the unit is degrees. The vertical axis of FIG. 36 shows the intensity distribution in the xz cross section of light, and the unit is an arbitrary unit representing the relative intensity in Example 4. According to FIG. 36, the maximum diffusion angle is about ± 19 degrees, and the shape of the intensity distribution shows a steep near this angle.

FIG. 37 is a diagram showing the intensity distribution in the yz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of Example 4 has passed through the diffusing element. The horizontal axis of FIG. 37 indicates the diffusion angle in the yz cross section, and the unit is degrees. The vertical axis of FIG. 37 shows the intensity distribution in the yz cross section of light, and the unit is an arbitrary unit representing the relative intensity in Example 4. According to FIG. 37, the maximum diffusion angle is about ± 10 degrees, and the shape of the intensity distribution shows a steep near this angle.

FIG. 38 is a diagram showing the intensity distribution in the xz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of the modified example of Example 4 passes through the diffusing element. In the modified example of the fourth embodiment, the positions and heights of the grid points of the fourth embodiment are dispersed by the above-mentioned method. The horizontal axis of 38 in the figure indicates the diffusion angle in the xz cross section, and the unit is degrees. The vertical axis of FIG. 38 shows the intensity distribution in the xz cross section of light, and the unit is an arbitrary unit representing the relative intensity in the modified example of Example 4.

FIG. 39 is a diagram showing the intensity distribution in the yz cross section after the parallel light incident perpendicularly to the xy plane of the diffusing element of the modified example of Example 4 passes through the diffusing element. The horizontal axis of 39 in the figure indicates the diffusion angle in the yz cross section, and the unit is degrees. The vertical axis of FIG. 39 shows the intensity distribution in the yz cross section of light, and the unit is an arbitrary unit representing the relative intensity in the modified example of Example 4.

According to FIGS. 36 to 39, the shape of the light intensity distribution by the diffusion element of Example 4 and its modified example is 0 when the absolute value of the diffusion angle is larger than the maximum value, and is 0 when the absolute value is greater than or equal to the maximum value. The shape is close to the ideal rectangular shape that is uniform. Comparing FIG. 39-39 with FIG. 36-37, the illuminance distribution in FIG. 39-39 is more uniform than the illuminance distribution in FIG. 36-37.

Characteristics of the shape of the diffusing element of Example 1-Example 4 According to FIGS. 17, 23, 28 and 33, _{the shape of h 1} (x) of Example 1-Example 4 is smooth and the x-axis. Symmetrical with respect to. At x = 0, h ₁ (x) has the maximum value.

18, according to FIG. 24, 29 and 34, the absolute value of the first derivative of h ₁ (x) is 0 in x = 0 corresponding to the maximum value of h ₁ (x), the absolute of x It increases as the value increases and reaches the maximum value, and then decreases to 0 as the absolute value of x increases. The absolute value of the first derivative of h ₁ (x) is equal to the absolute value of the tangent of the tangent angle. Since the absolute value of the diffusion angle becomes the maximum when the tangent angle becomes the maximum, the maximum value of the absolute value of the diffusion angle is determined by the maximum value of the absolute value of the first derivative of _{h 1 (x).}

19, FIG. 25, according to FIGS. 30 and 35, in the region has a smaller absolute value of the absolute value than the x of x corresponding to the maximum value of the absolute value of the first derivative of h ₁ (x), h ₁ (x second derivative of) is zero or negative, in the region having a larger absolute value of x than the absolute value of x corresponding to the maximum value of the absolute value of the first derivative of h ₁ (x), h ₁ of (x) second derivative is zero or a positive second derivative of h ₁ (x) is discontinuous at x corresponding to the maximum value of the absolute value of the first derivative of h ₁ (x). That is, the absolute value of the first derivative of h ₁ (x) in the x-coordinate of the respective discontinuity point second derivative of h ₁ (x) indicates the maximum value, the absolute value of the diffusion angle of the value xz section Corresponds to the maximum value of.

The absolute value of the diffusion angle θ changes according to the tangent angle, the absolute value of _{the first-order differential of h 1} (x) is equal to the absolute value of the tangent of the tangent angle, and the maximum value of the absolute value of the diffusion angle is h ₁ (x). Determined by the absolute value of the first-order differential of. Further, the second-order differential of h ₁ (x) is discontinuous at x corresponding to the maximum value of the absolute value of the first derivative of h ₁ (x), the second order derivative of the code of h ₁ (x) is h _It changes at x corresponding to the maximum absolute value of the first derivative of 1 (x). This means that when the diffusion angle is plotted against x, the diffusion angle changes sharply at x corresponding to the maximum absolute value of the first derivative. As a result, the shape of the light intensity distribution plotted against the diffusion angle in the xz cross section changes sharply near the maximum value of the absolute value of the diffusion angle in the xz cross section. As described above, the light has almost uniform intensity at the absolute value of the diffusion angle equal to or less than the maximum value of the absolute value of the diffusion angle in the xz cross section, and the diffusion angle exceeds the maximum value of the absolute value of the diffusion angle in the xz cross section. In the absolute value of, a diffusing element having characteristics close to the ideal characteristics in which the light intensity is 0 can be obtained.

_{H 2} (y) of Examples 1-4 also has the same shape as _{h 1 (x).} That is, _{the shape of h 2} (y) is smooth and symmetric with respect to the y-axis. At y = 0, h ₂ (y) has the maximum value. the absolute value of the first derivative of h ₂ (y), in the y = 0 corresponding to the maximum value of h ₂ (y) is 0, it reaches the increased maximum value as the absolute value of y increases, After that, as the absolute value of y increases, it decreases to 0. In the region having a small absolute value of y than the absolute value of y corresponding to the maximum value of the absolute value of the first derivative of h ₂ (y), ₂ differential of h ₂ (y) is zero or negative, h ₂ In the region where the absolute value of y is greater than the absolute value of y, which corresponds to the maximum absolute value of the first derivative of _{(y), the second derivative of h 2} (y) is 0 or positive, h ₂ (y). The second derivative of) is discontinuous in y, which corresponds to the maximum absolute value of the first _{derivative of h 2 (y).} That, h ₂ absolute value of the first derivative of h ₂ (y) in each of the x coordinate of the point of discontinuity second derivative of (y) is the maximum value, the absolute value of the diffusion angle of the value yz section Corresponds to the maximum value of. Therefore, light has almost uniform intensity at the absolute value of the diffusion angle equal to or less than the maximum value of the absolute value of the diffusion angle in the yz cross section, and the absolute value of the diffusion angle exceeding the maximum value of the absolute value of the diffusion angle in the yz cross section. In terms of value, a diffusing element having characteristics close to the ideal characteristic in which the light intensity is 0 can be obtained.

が、特徴的な形状を有する。実施例１−４においては、g(x,y)及び- g(x,y)の少なくとも一方で表される形状が式（３）または式（４）に示すようにxy平面上に配置されている。一般的に、拡散素子はz=g(x,y)で表される形状及びz=-g(x,y) で表される形状の少なくとも一方のxy平面上の平行移動によって得られた複数の形状から構成してもよい。拡散素子のｘｙ面上への射影面積に対するxy面上の平面の面積の比率が所定値以下となるようにxy平面上に上記の複数の形状を配置することによって理想の特性に近い特性の拡散素子が得られる。上記の所定値は１％である。 Examples 1-4 are characterized by the shapes _{of h 1} (x) and h _{2 (y).} That is,

However, it has a characteristic shape. In Examples 1-4, the shapes represented by at least one of g (x, y) and −g (x, y) are arranged on the xy plane as shown in the formula (3) or the formula (4). ing. In general, the diffusing element is a plurality of diffusing elements obtained by translation on at least one xy plane of the shape represented by z = g (x, y) and the shape represented by z = -g (x, y). It may be composed of the shape of. By arranging the above-mentioned plurality of shapes on the xy plane so that the ratio of the area of the plane on the xy plane to the projected area on the xy plane of the diffusing element is equal to or less than a predetermined value, diffusion of characteristics close to the ideal characteristics is performed. The element is obtained. The above predetermined value is 1%.

A method for manufacturing a diffusion element according to the present invention will be described.

FIG. 40 is a flow chart showing a method for manufacturing a diffusion element according to the present invention.

In step S2010 of FIG. 40, the functions z = g (x, y) = h ₁ (x) · h ₂ (y) are defined.

をその境界、すなわち基準の矩形の辺とすると、以下の関係が成立する。

のとき

のとき

The shape of the reference rectangle is represented by z = g (x, y). The origin of the (x, y) coordinates is the center of the reference rectangle. Area within a rectangle relative to S,

Let be the boundary, that is, the side of the reference rectangle, and the following relationship holds.

When

When

で表され、

の1階微分が

において連続であり、該頂点のｘ座標において０であり、ｘ座標が該頂点のｘ座標より小さい領域の１階微分が正でｘ座標が該頂点のｘ座標より大きい領域の１階微分が負であり、

の2階微分が、ｘ座標が該頂点のｘ座標より小さい領域及びｘ座標が該頂点のｘ座標より大きい領域においてそれぞれ単一の不連続な点を有し、

の1階微分が

において連続であり、該頂点のｙ座標において０であり、ｙ座標が該頂点のｙ座標より小さい領域の１階微分が正でｙ座標が該頂点のｙ座標より大きい領域の１階微分が負であり、

の2階微分が、ｙ座標が該頂点のｙ座標より小さい領域及びｙ座標が該頂点のｙ座標より大きい領域においてそれぞれ単一の不連続な点を有する。 z = g (x, y) has a single vertex in the rectangle, and z is from any point to the vertex along a straight line connecting any point on the side of the rectangle to the vertex. Monotonically increasing,

Represented by

The first derivative of

Is continuous, 0 in the x-coordinate of the vertex, the first derivative of the region where the x-coordinate is smaller than the x-coordinate of the vertex is positive, and the first-order derivative of the region whose x-coordinate is larger than the x-coordinate of the vertex is negative. And

The second derivative of the above has a single discontinuous point in a region where the x-coordinate is smaller than the x-coordinate of the vertex and in a region where the x-coordinate is larger than the x-coordinate of the vertex.

The first derivative of

Is continuous, 0 in the y-coordinate of the vertex, the first derivative of the region where the y-coordinate is smaller than the y-coordinate of the vertex is positive, and the first-order derivative of the region where the y-coordinate is larger than the y-coordinate of the vertex is negative. And

The second derivative of the above has a single discontinuous point in a region where the y-coordinate is smaller than the y-coordinate of the vertex and in a region where the y-coordinate is larger than the y-coordinate of the vertex.

h ₁ (x) and h ₂ (y) may be the functional expressions shown in the examples.

In step S2020 of FIG. 40, h ₁ (x) 2 floor absolute first floor diffusion angle of maximum xz cross section of the absolute value of the differential of h ₁ (x) in the x-coordinate of the at least one discontinuity of the derivative of corresponding to the desired maximum value, the diffusion of the second floor maximum yz cross section of the absolute value of the first derivative of h ₂ (y) in the y-coordinate of the at least one discontinuity of the derivative of h ₂ (y) Adjust the derivatives _{of h 1} (x) and h ₂ (y) to correspond to the desired maximum absolute value of the angle.

As explained with reference to FIG. 14, the maximum value of the incident angle θin is determined from Eq. (2) by the maximum absolute value of the first derivative of _{h 1} (x) and h _{2 (y), and further Eq.} From (1), the maximum value of the absolute value of the diffusion angle θ can be obtained. Therefore, the desired maximum value of the absolute value of the diffusion angle θ can be realized by adjusting the respective coefficients of _{h 1} (x) and h _{2 (y).}

In step S2030 of FIG. 40, the entire diffusing element is translated by translation on at least one xy plane of the shape represented by z = g (x, y) and the shape represented by z = -g (x, y). Determine the shape of.

The overall shape may be a shape represented by the formula (3) or the formula (4).

Claims (10)

The smooth function in the rectangle whose origin is the center of the rectangle having the side of the length s in the x direction and the side of the length t in the y direction on the (x, y) plane is z = g (x, y). As a plurality of shapes obtained by parallel movement on at least one xy plane of the shape represented by z = g (x, y) and the shape represented by z = -g (x, y). In the xz cross section, the angle formed by the light beam emitted from the diffusing element in the z-axis direction is defined as the absolute value of the diffusion angle in the xz cross section, and in the yz cross section, the angle formed by the light beam emitted from the diffusing element in the z-axis direction is defined as the absolute value. A diffusion element configured to obtain a desired maximum value of the absolute value of the diffusion angle of the xz cross section and a desired maximum value of the absolute value of the diffusion angle of the yz cross section as the absolute value of the diffusion angle of the yz cross section. ,
On the sides of the rectangle

Z = g (x, y) has a single vertex in the rectangle, and the vertex from the arbitrary point along the straight line connecting the arbitrary point on the side of the rectangle and the vertex. Z increases monotonically until

Represented by

The first derivative of

Is continuous, 0 in the x-coordinate of the vertex, the first derivative of the region where the x-coordinate is smaller than the x-coordinate of the vertex is positive, and the first-order derivative of the region whose x-coordinate is larger than the x-coordinate of the vertex is negative. And

The second derivative of the above has a single discontinuous point in a region where the x-coordinate is smaller than the x-coordinate of the vertex and in a region where the x-coordinate is larger than the x-coordinate of the vertex.

The first derivative of

Is continuous, 0 in the y-coordinate of the vertex, the first derivative of the region where the y-coordinate is smaller than the y-coordinate of the vertex is positive, and the first-order derivative of the region where the y-coordinate is larger than the y-coordinate of the vertex is negative. And

The second derivative of the above has a single discontinuous point in a region where the y-coordinate is smaller than the y-coordinate of the vertex and in a region where the y-coordinate is larger than the y-coordinate of the vertex.
h ₁ such that the desired maximum value of the second order absolute value of the first derivative of the diffusion angle of the absolute value xz section of h ₁ (x) in the x-coordinate of the at least one discontinuity of the derivative of (x) is obtained stipulated in, h ₂ 2 floor desired maximum value of the absolute value of the diffusion angle of the absolute value yz cross section of the first derivative of h ₂ (y) in the y-coordinate of the at least one discontinuity of the derivative of the (y) A diffusing element defined so that The overall shape is

Represented by, m and n are integers indicating the positions of rectangles in the x and y directions, respectively, the minimum value of m and n is 0, and the maximum value of m is determined by the dimension of the diffusion element in the x direction. The diffusion element according to claim 1, wherein the maximum value of n is determined by the dimension of the diffusion element in the y direction. The overall shape is

Represented by, m and n are integers indicating the positions of rectangles in the x and y directions, respectively, the minimum value of m and n is 0, and the maximum value of m is determined by the dimension of the diffusion element in the x direction. The diffusion element according to claim 1, wherein the maximum value of n is determined by the dimension of the diffusion element in the y direction. Assuming that N and M are natural numbers of 2 or more, i and j are natural numbers, and A _i and B _i are constants.

Is a polynomial of degree 2 or higher x

Represented by

Is a polynomial of degree 2 or higher

The diffusion element according to any one of claims 1 to 3 represented by.

as well as

The diffusion element according to claim 4, wherein is an even-order polynomial. The diffusion element according to any one of claims 1 to 5, wherein the ratio of the area of the plane on the xy plane to the projected area on the xy plane is 1% or less. A convex quadrangle is formed by moving the vertices of each rectangle of the diffusion element according to claim 1 within a predetermined range on the xy plane, and a new shape of the diffusion element is formed in the convex quadrangle. A diffusing element defined so that z at the first point is equal to z of the diffusing element according to any one of claims 1 to 6 at the second point in each outer rectangle corresponding to the first point. .. A diffusion element obtained by multiplying the z coordinate in each rectangle of the diffusion element according to any one of claims 1 to 7 by γ, and changing the value of γ in the range of 0.9 to 1.1 for each rectangle. Diffusing element. The shape is provided on a curved surface, and the shape is a projection of the shape on the xy surface of the diffusion element according to any one of claims 1 to 8, and the projection projects the xy plane onto the curved surface. Diffusing element. z = g (x, y) is a smooth function in the (x, y) plane with the center of the rectangle having the side of the length s in the x direction and the side of the length t in the y direction as the origin. As a plurality of shapes obtained by parallel movement on at least one xy plane of the shape represented by z = g (x, y) and the shape represented by z = -g (x, y). In the xz cross section, the angle formed by the light beam emitted from the diffusing element in the z-axis direction is defined as the absolute value of the diffusion angle in the xz cross section, and in the yz cross section, the angle formed by the light beam emitted from the diffusing element in the z-axis direction is defined as the absolute value. A method for manufacturing a diffusion element configured to obtain a desired maximum value of the absolute value of the diffusion angle of the xz cross section and a desired maximum value of the absolute value of the diffusion angle of the yz cross section as the absolute value of the diffusion angle of the yz cross section. And
On the sides of the rectangle

Z = g (x, y) has a single vertex in the rectangle, and the vertex from the arbitrary point along the straight line connecting the arbitrary point on the side of the rectangle and the vertex. Z increases monotonically until

Represented by

The first derivative of

Is continuous, is 0 at the vertex, the first derivative of the region whose x-coordinate is smaller than the x-coordinate of the vertex is positive, and the first derivative of the region whose x-coordinate is larger than the x-coordinate of the vertex is negative.

The second derivative of the above has a single discontinuous point in a region where the x-coordinate is smaller than the x-coordinate of the vertex and in a region where the x-coordinate is larger than the x-coordinate of the vertex.

The first derivative of

Is continuous, 0 in the y-coordinate of the vertex, the first derivative of the region where the y-coordinate is smaller than the y-coordinate of the vertex is positive, and the first-order derivative of the region where the y-coordinate is larger than the y-coordinate of the vertex is negative. And

The second derivative of z = g (x, y) has a single discontinuous point in the region where the y-coordinate is smaller than the y-coordinate of the vertex and in the region where the y-coordinate is larger than the y-coordinate of the vertex. Steps to determine and
in the xz cross section, h ₁ 2 floor at least one of a desired maximum value of the first-order absolute value of the diffusion angle of the absolute value xz cross section of the derivative of h ₁ (x) in the x-coordinate of the discontinuity of the derivative of (x) corresponds to, h ₂ 2 floor desired maximum value of the absolute value of the diffusion angle of the absolute value yz cross section of the first derivative of h ₂ (y) in the y-coordinate of the at least one discontinuity of the derivative of the (y) And the step of adjusting the coefficients _{of h 1} (x) and h ₂ (y) to correspond to
Diffusion, including the step of defining the overall shape by translation on at least one of the xy planes of the shape represented by z = g (x, y) and the shape represented by z = -g (x, y). Method of manufacturing the element.

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